I was there last weekend for the bike race. We go about 3-4 times a year. For a family, I would recommend the Lost Mine and The Window trails while in the park, as they provide great views without overly taxing the kids.
How much time are you spending in the park and how much time are you spending doing other things in the West Texas area? IMO, you could spend an entire week in the park alone, but probably not with young kids.
If you head out there through Marfa, attend a Star Party at McDonald Observatory in Fort Davis, which is just 25 miles north of Marfa. If you stay overnight in Fort Davis, then there's the Limpia Hotel. If you stay overnight in Marfa, stay in the Paisano. In Marathon, stay at the Gage.
As mentioned above, swim in the pool at Balmorhea State Park.
If you want some great pizza for the kids (and adults) for dinner (only open for dinner), visit Long Draw Pizza on Highway 170, just west of Terlingua on the left. Say hello to Nancy. She is a bit gruff, but makes a darn good pizza.
If you want to do a river tour or guided mountain bike ride, the guys at Desert Sports in Terlingua are the ones to use.
Above all, stop in the ranger station at Panther Junction and talk to the staff. They are always going to be a great source of info. Plus, Ranger Dean is a great guy.
Have fun.